Hi 

i have a set of RNAseq data with unbalanced batch effect (see table below). Batch 1 was made of single indexed kit and sequenced at time 1, while batch 2 was made of dual indexed kit and sequenced independently from batch 1.

From my exploratory analysis, I noticed batch 1 samples and batch 2 samples are clustered independently from each other. https://ibb.co/meWjcz

Thus, on my DE analysis design, I used batch as covariant to evaluate the batch effect DE. 

groups <- relevel(groups, ref="Naive_KO")
batch <- relevel(batch,ref="1")
design <- model.matrix(~batch+groups, data=y$samples)
y_filtered <- estimateDisp(y_filtered,design)
fit <- glmQLFit(y_filtered, design, robust=T)

I found 24439 genes were differentially expressed btw batch 1 and batch 2.

#### batch effect 
batch_DE <- glmQLFTest(fit, coef=2)
FDR <- p.adjust(batch_DE$table$PValue, 'fdr')
sum(FDR < 0.05)
# 24439

My questions:

1. since Naive has only batch 2 samples no batch 1 samples, Can 24439 batch DE genes be caused by difference between other Th and Naive? In the linear regression, ~batch+groups , we assume batch and group are independent. theoretically, those 24439 genes should be independent of group difference, but this unbalanced design really bothers me.

2. Will this unbalance design affect differential analysis between groups? for example, comparing Th1_WT to Naive_WT. 

That's not what you would normally call an unbalanced design. Well, it is unbalanced (meaning you have different numbers of samples in some of the groups), but what you are talking about is confounding. The naive samples are completely confounded with batch, so you cannot say if any differences between those samples and any of the other samples is due to a batch effect or real biological differences.

That, unfortunately, is an unfixable problem.